Robust swing leg controller under large disturbances

ABSTRACT

Local swing leg control was developed that takes advantage of segment interactions to achieve robust leg placement under large disturbances while generating trajectories and joint torque patterns similar to those observed in human walking and running. The results suggest the identified control as a powerful alternative to existing swing leg controls in humanoid and rehabilitation robotics. Alternatively, a detailed neuromuscular model of the human swing leg was developed to embody the control with local muscle reflexes. The resulting reflex control robustly places the swing leg into a wide range of landing points observed in human walking and running, and it generates similar patterns of joint torques and muscle activations. The results suggest an alternative to existing swing leg controls in humanoid and rehabilitation robotics which does not require central processing.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional of US Nonprovisional application Ser.No. 14/470/277 filed Aug. 27, 2014, which claims priority to U.S.Provisional Application Ser. No. 61/959,564, titled ROBUST SWING LEGCONTROLLER UNDER LARGE DISTURBANCES, filed Aug. 27, 2013, and to U.S.Provisional Application Ser. No. 61/959,561, titled MUSCLE-RELFEXCONTROL OF ROBUST SWING LEG PLACEMENT, filed Aug. 27, 2013, each ofwhich are incorporated by reference herein in their entirety.

STATEMENT REGARDING FEDERALLY-SPONSORED RESEARCH AND DEVELOPMENT

This invention was made with government support under the NationalScience Foundation EEC 0540865 and National Institute of Health1R01HD075492-01. The government has certain rights in this invention.

BACKGROUND

Swing leg placement is vital to stability in legged robots and animals.Without placing the feet into proper target points on the ground, leggedsystems fail to balance dynamically. These targets have been identifiedwith simplified point-mass models including the linear inverted pendulumfor standing and walking, and the spring-mass system for running. Themodels predict foot placement targets which stabilize gait in responseto a disturbance such as an external push or an unexpected change in theground level. However, they do not reveal how the segmented legs ofhumans and humanoids can actually reach these targets.

The most common approach to generating swing leg motions in humanoidsuses trajectory planning and tracking. In this approach, trajectoriesfor all leg joints are planned either based on optimization overdeviations from the foot placement targets or by spline interpolationbetween consecutive placement targets. Once generated, these referencetrajectories are tracked via proportional-derivative control at thejoint levels. Planning and tracking of swing-leg trajectories requirescentral control over all leg joints, which limits the application ofthis approach to powered prosthetic limbs which replace only part of thehuman body.

Although alternative approaches have been explored in rehabilitationrobotics, tracking predefined joint patterns remains the state of theart in the control of powered artificial legs. For instance, current legprostheses mimic human joint impedances that have been recorded inexperiments. Bound to these predefined patterns, handling gaitdisturbances still requires event detection, automatic classification,and the implementation of deliberate joint trajectories to counter thesedisturbances, hampering practical implementations of autonomous poweredlegs that achieve robust swing placement under large disturbances.

Animal and human legs by contrast demonstrate robust swing placementwith remarkable autonomy. From early work on mesencephalic cats torecent investigations on paralyzed cats and rats with drugadministration and epidural stimulation, experiments have shown thatanimals can seamlessly adapt their leg behavior throughout stance andswing, to different speeds and gaits without central planning by thebrain. These observations suggest that a substantial part of leg controlin animal and human locomotion is generated by spinal circuits whichadapt to changes in the environment.

BRIEF SUMMARY OF THE INVENTION

A control for swing leg motions is described herein, inspired byobservations on local control in animal and human locomotion. It isbased on local feedbacks and does not require predefined swing legtrajectories to robustly place the leg into target points on the ground.In one embodiment, a control was developed guided by the segmentdynamics of a double pendulum. The control is structured around asequence of three tasks that include flexing the leg into a clearancelength, advancing the leg into a target angle, and extending it untilground contact. Although this sequence can be enforced with stricttrajectory tracking, energy efficient and modular artificial legs inrehabilitation robotics was targeted and hence the developed controltakes advantage of passive swing leg dynamics and decouples individualhip and knee controls wherein the motion of the hip and the knee jointsare determined without enforcing reference trajectories of either thehip or the knee joint. Thus, the developed control does not requiretracking reference trajectories of either the hip or the knee joint. Theperformance of the control in simulations was tested with a moreanthropomorphic swing leg that considers human-like segment mass andinertia distribution as well as the effect of translational hipacceleration. It was demonstrated that the identified control canachieve swing leg placement into a large range of target points, andthat this placement is robust to disturbances in initial conditions andto sudden changes in the target during swing, and that the resultingswing leg trajectories and joint torque patterns compare to those ofhuman walking and running.

An alternative embodiment of a control for swing leg motions wasdeveloped based on local feedbacks and does not require predefined swingleg trajectories to robustly place the leg into target points on theground. To compare the identified control with human swing leg behaviorat the level of muscle activations and to prepare a transfer to poweredprosthetic legs that react like human limbs, a neuromuscular controlmodel of the human leg in swing was developed that embodies theidentified control with local reflexes. The resulting reflex controlrobustly places the swing leg into target angles from 50 deg to 75 degwhich cover observed landing leg angles for a wide range of humanwalking and running speeds. In addition, the control generates swingpatterns that share the main features of human swing leg patterns forthe ankle trajectory, joint torques, and muscle activations. The exampleembodiments described herein suggest an alternative to existing swingleg controls including, but not limited to, humanoid and rehabilitationrobotics which does not require central processing.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A and 1B illustrate swing leg models: (A) Conceptual doublependulum model with point masses at the segment ends; and (B) Morerealistic swing leg model with human-like segment mass distribution andhip translational accelerations as external input;

FIGS. 2A and 2B illustrate swing leg control. (A) Sequence of naturalcontrol tasks for reaching a target placement while guaranteeing footground clearance. (B) Functional relationship between α and φ_(h) andφ_(k). With γ=90−φ_(k)/2 and β=180−γ—φ_(h), α relates to φ_(h) and φ_(k)as

${\alpha = {\varphi_{h} - \frac{\varphi_{k}}{2}}};$

FIGS. 2C and 2D illustrate individually the knee control and the hipcontrol in a typical swing phase;

FIG. 3A is a representation of a simulation model of the presentinvention;

FIG. 3B is a plot of swing leg placement into arbitrary targets underlarge variation in initial conditions. The error Δα=α_(tgt)−α_(l)between the target angle and the achieved landing angle is shown as acolor code for a large range of initial hip and knee velocities thatcover the initial joint velocities observed in human locomotion from0.65 ms⁻¹ to 5.5 ms⁻¹;

FIGS. 4A-C illustrates the observed and predicted swing leg patterns inwalking, respectively. The ankle trajectories (A), hip and knee torques(B&C) during multiple swing phases (individual traces) are comparedbetween human walking and model prediction at four different walkingspeeds (color coded). For the model, the initial joint positions andspeeds as well as the hip translational accelerations are taken from thecorresponding human swing motions. The coordinates of the foot point inA are given with respect to a world frame that originates at the initialposition of the hip. The torques in B and C are normalized to percent ofbody weight times leg length (% bwll);

FIGS. 5A-C illustrates the observed and predicted swing leg patterns inrunning, respectively. See caption of FIG. 4 for explanations. Note thatfor only one swing at 3.5 ms⁻¹, the model engaged knee stop (knee torquespike at end.);

FIGS. 6A-C illustrates the Reaction to disturbances during swing. Thereaction to disturbances during swing is shown for large changes in thetarget leg angle α and during simulated obstacle encounters forcharacteristic swing phases with initial conditions that match humanwalking at 1.3 ms⁻¹. Undisturbed swing phases are shown in gray anddisturbed ones in black. (A) The target angle (dashed line) is changedat 75 ms into the swing from 50 deg to 90 deg (left column) and viceversa (right column). The arrows mark the foot point position at thetime of change. (B) An external impulse of 15 Ns is applied to the footpoint in early (left) and late swing (right), resulting in an elevatedfoot point trajectory and premature landing, respectively. The arrowsindicate the start and end of the force application;

FIG. 7 is an overview of the system of the present invention;

FIG. 8 is an implementation of the key modules of the system;

FIG. 9 is a system schematic of the knee joint control system of thepresent invention;

FIG. 10 is a system schematic of the hip joint control system of thepresent invention;

FIG. 11 is a logic flow diagram of one embodiment of the presentinvention;

FIGS. 12A-B illustrates the neuromuscular model for swing leg placement.(A) The ankle is controlled by the soleus (SOL), gastrocnemius (GAS),and tibialis anterior (TA) muscles. The hip is flexed and extended bymonoarticular hip flexor (HFL) and glutei (GLU) muscle groups. (B) Theknee control is divided into the three tasks of the previouslyidentified control. (i) Initial flexion is generated by themonoarticular biceps femoris short head muscle (BFsH). (ii) The knee isconstrained by rectus femoris (RF) during hyperflexion and by BFsHduring extension. (iii) The hamstring muscle group (HAM) and the vastiigroup (VAS) brake and extend the leg. In addition, HAM recruits GAS andBFsH to prevent knee hyper-extension;

FIG. 13 illustrates the swing leg placement error for the neuromuscularcontrol model. The leg is hinged and the initial configuration is set toφ_(m)=220 deg, φ_(k,0)=175 deg (α₀=132.5 deg), and φ_(a,0)=120 deg. Theclearance leg length is set tol_(cir)=5 cm;

FIGS. 14A-F show the observed and predicted swing leg patterns inwalking and running. The ankle trajectories (A,D), hip and knee torques(B,C,E,F) of multiple swing phases (individual traces) are comparedbetween human and model at different speeds (color coded). For themodel, the initial joint positions and speeds as well as the hiptranslational accelerations are taken from the corresponding human swingmotions. The target angle is set to the observed (average) landing angleα_(tgt)=70 deg. The ankle trajectories are given with respect to a worldframe that originates at the initial position of the hip. The torquesare normalized to percent of body weight times leg length (% bwll);

FIGS. 15A-C show the observed and predicted muscle activations inwalking and running. Steady-state patterns of muscle activations duringswing are shown for hip (A), knee (B) and ankle muscles (C). Comparedmuscles: (i) iliacus (ii) upper gluteus maximum, (iii) semimembranosis,and (iv) vastus lateralis;

FIG. 16 is an overview of one aspect of the neuromuscular control modelof the present invention illustrating the process for neuromuscularestimates of leg angle and leg angular speed;

FIG. 17 is an overview of another aspect of the neuromuscular controlmodel of the present invention illustrating the process forneuromuscular estimates of leg length and leg lengthening speed;

FIG. 18 is an overview of yet another aspect of the neuromuscularcontrol model of the present invention illustrating the process for kneejoint control;

FIG. 19 is an overview of yet another aspect of the neuromuscularcontrol model of the present invention illustrating the process for hipjoint control;

FIG. 20 is an overview of yet another aspect of the neuromuscularcontrol model of the present invention illustrating the process fortorque contribution of biarticular muscle;

FIG. 21 is an overview of yet another aspect of the neuromuscularcontrol model of the present invention illustrating the process fortorque contribution of monoarticular hip muscle;

FIG. 22 is an overview of yet another aspect of the neuromuscularcontrol model of the present invention illustrating the process fortorque contribution of monoarticular knee muscle;

FIG. 23 is an overview of yet another aspect of the neuromuscularcontrol model of the present invention illustrating the process fordesired hip torque computation; and

FIG. 24 is an overview of yet another aspect of the neuromuscularcontrol model of the present invention illustrating the process fordesired knee torque computation.

DETAILED DESCRIPTION OF THE INVENTION

Swing Leg Model

In human and humanoids, leg placement is largely achieved by the motionof the hip and knee while the ankle contribution can be neglected. Todevelop intuition about the control strategies for swing leg placement,the classic double pendulum with the thigh and shank represented asmassless rods of lengths l_(t) and l_(s) with point masses m_(t) and m,attached to their ends was used in one embodiment (FIG. 1A). The hip isconnected to an immovable trunk at the origin of the world frame, andthe joint angles φ_(h) and φ_(k) are measured as shown in FIG. 1A. Theresulting equations of motion are:

((m _(t) +m _(s))l _(t) −m _(s) l _(s) cos φ_(k))l _(r)φ_(h)=τ_(h)+τ_(k)−m _(s) l _(t) l _(s) cos φ_(k){umlaut over (φ)}_(k) +m _(s) l _(s) l_(t) sin φ_(k)({dot over (φ)}_(k)−{dot over (φ)}_(h))²+(m _(t) +m _(s))l_(t) g sin φ_(h)  (1)

m _(s) l _(s){umlaut over (φ)}_(k)=τ_(k) +m _(s) l _(s)(l _(s) −l _(t)cos φ_(k)){umlaut over (φ)}_(h) +m _(s) l _(s) l _(t) sin φ_(k){dot over(φ)}_(h) ² −m _(s) l _(s) g sin(φ_(k)−φ_(h))  (2)

for the hip and knee, respectively, where τ_(h) and τ_(k) are theapplied hip and knee torques.

In addition to the conceptual model, the performance of the control witha more realistic simulation model of human swing motions was tested(FIG. 1B). In this second model, the segment inertial properties arebased on anthropomorphic data obtained from scaling tables for a humanwith a body weight and height of 80 kg and 180 cm (m_(t)=7 kg, m_(s)=4.3kg, d_(t)=21.7 cm, d_(s)=30.3 cm, l_(t)=43 cm, l_(s)=43 cm). Moreover,the model includes a knee stop realized by a restoring torque:

$\begin{matrix}{\tau_{k}^{res} = \left\{ \begin{matrix}{{{k_{\varphi}\left( {\varphi_{k} - \varphi_{\max}} \right)}\left( {1 + {{\overset{.}{\varphi}}_{k}/{\overset{.}{\varphi}}_{\max}}} \right)},} & \begin{matrix}{{\overset{.}{\varphi}}_{k} > {- {\overset{.}{\varphi}}_{\max}}} \\{{\overset{.}{\varphi}}_{k} > \varphi_{{ma}x}}\end{matrix} \\{0,} & {otherwise}\end{matrix} \right.} & (3)\end{matrix}$

(φ_(max)=175 deg, {dot over (φ)}_(max)=0.01 rads⁻¹, k_(φ)=17.2 Nmrad⁻¹)and accounts for hip translational accelerations (α_(x), α_(y)) in latercomparisons to human swing phases in steady walking and running.

Modular Local Control

In addition to the fundamental goal placing the foot into target points,the swing leg motion is subject to the constraint that the foot pointneeds to clear the ground or an obstacle. We represent both, theplacement goal and the clearance constraint, by two control variables,the target leg angle α_(tgt) and the clearance leg length l_(clr),respectively (FIGS. 2A and 2C). Assuming equal segment lengthsl_(t)=l_(s) (good approximation for human legs) in the remainder of thispaper, the leg angle is given by

$\alpha = {\varphi_{h} - \frac{\varphi_{k}}{2}}$

and the lug length resolves to

$l = {2l_{t}\sin \frac{\varphi_{k}}{2}}$

(FIG. 2B).

FIG. 2A outlines a natural sequence of three control tasks whichreflects the objective and constraint. First, starting at the groundlevel from an initial leg angle α₀, the clearance constraint requiresthe leg to flex to at least the clearance length l_(clr) (reached at P).Second, the control focus shifts to advancing the swing leg to thetarget angle α_(tgt) (reached at Q). And the final task is to extend theleg until ground contact.

Although this sequence of control tasks can be strictly enforced withclassical state feedback control, tracking predefined trajectories isavoided for two reasons. Similar to humans, we seek to take advantage ofthe passive dynamics that the swing leg provides to lessen the requiredtorques. In addition, we seek decoupled joint controls as much aspossible to modularize the control. Both goals target autonomous andmodular replacement legs in rehabilitation robotics. As a consequence,the swing leg control is structured around functionally distinct hip andknee joint controls.

FIG. 2C outlines the various distinct phases of the knee control of thetypical swing phase: flex, damp, stop, and extend. The Flex phase beginsfrom the initial point of raising a foot in contact with the ground tothe point where the current leg length is equal to or less than theclearance leg length l_(clr), thereby beginning the Damp phase. The Dampphase dampens the motion of the leg along the leg lengthening axismodulated by how close the leg angle is to the target angle and by howfast the leg angle is moving towards the target angle according toequation 7, until the current leg angle is smaller than the thresholdangle, which initiates the Stop phase. The Stop phase reduces andreverses the leg angular speed in preparation of the Extend phase thatwill lower the foot on to the target position causing the foot to movebackwards when the leg is extended. FIG. 2D further illustrates thevarious phases of the hip control of the typical swing phase: move totarget and move & compensate. The Move to target phase begins from theinitial point of raising a foot in contact with the ground. In thisphase the hip control seeks to place the leg into the target angle. Whenthe leg angle reaches the threshold leg angle, the hip control switchesto the Move & Compensate phase in which the torque generated by the hipcontrol is augmented with a compensation torque that compensates for theeffect of torque produced around the knee on the hip.

A. Hip Control

The hip control is active throughout the swing and its primary functionis to move the leg into the target angle α_(tgt). The specific controlinput τ_(h) ^(α) is given by

τ_(h) ^(α) =k _(p) ^(α)(α_(tgt)−α)−k _(d) ^(α){dot over (α)}  (4)

where k_(p) ^(α) and k_(d) ^(α) are proportional and derivative gains,respectively. Note that a negative input tends to flex the hip. Inaddition to the angle control, the hip control receives a second inputτ_(h) ^(iii) from the knee control,

τ_(h)=τ_(h) ^(α)+τ_(h) ^(iii),  (5)

during the last, leg extension stage in the control sequence (afterreaching Q). The purpose of τ_(h) ^(iii) is detailed in the next sectionon knee control. It is the only crossover input between the joints.

B. Knee Control

The knee control's primary function is to regulate leg length. However,due to the influence of the knee angle on both, leg length and legangle, the control is more involved. It is separated into the threenatural control tasks outlined before (FIG. 2A).

To accomplish the first control task of reaching a minimum clearancel_(clr) in the initial swing, we take advantage of the passive swing legdynamics. Equation 2 shows that while the Coriolis, centrifugal andgravitational terms always tend to extend the knee, a negative hipacceleration tends to flex the knee. The hip control (Eq. 4) generatesnegative hip acceleration initially to drive the leg into the targetangle. The resulting passive, negative knee acceleration sufficientlyovercomes the opposing Coriolis, centrifugal and gravitationalaccelerations as long as the leg angle α increases, α>0 or equivalently{dot over (φ)}_(k)<2{dot over (φ)}_(h) (backward motion of foot point).In that case, no input τ_(k) is required to flex the leg, as theincrease in a reinforces hip flexion control and, in turn, passive kneeflexion. If on the other hand {dot over (α)}<0, the passive knee flexionis no longer sufficient and the leg tends to scuff the foot. Thus weimplement active knee flexion control only in proportion to how fast theleg moves forward,

$\begin{matrix}{\tau_{k}^{i} = \left\{ {\begin{matrix}{{k^{i}\overset{.}{\alpha}},} & {\overset{.}{\alpha} \leqq 0} \\{0,} & {\overset{.}{\alpha} > 0}\end{matrix},} \right.} & (6)\end{matrix}$

where k^(i) is a proportional gain.

Once the leg length as shortened past the clearance length, l<l_(clr),the knee control switches to the second task of damping the knee so thatthe leg angle control by the hip can take full effect (Eq. 4). Werealize this task with a damping input

$\begin{matrix}{\tau_{k}^{ii} = \left\{ \begin{matrix}{{{- k^{ii}}{\overset{.}{\varphi}}_{k}},} & {{\overset{.}{\varphi}}_{k} \leqq 0} \\{{{- k^{ii}}{{\overset{.}{\varphi}}_{k}\left( {\alpha - \alpha_{tgt}} \right)}\left( {{\overset{.}{\varphi}}_{k} + \overset{.}{\alpha}} \right)},} & {{{{{\overset{.}{\varphi}}_{k} > 0}\&}{\overset{.}{\varphi}}_{k}} > {- \overset{.}{\alpha}}} \\{0,} & {otherwise}\end{matrix} \right.} & (7)\end{matrix}$

that is pure when the knee flexes ({dot over (φ)}_(k)≦0) and modulatedwhen it extends ({dot over (φ)}_(k)>0), with a proportional gain ofk^(ii). The implementation avoids the large torques that a precisetracking of l=l_(clr) would incur fighting the passive swing legdynamics (FIG. 2A). In particular, when the hip control stops pullingforward, all interaction terms in equation 2 create passive kneeextension. The first modulation term (α−α_(tgt)), enables this passiveextension when a approaches its target, easing the third control task.However, when the leg swings faster at higher speeds, passive kneeextension amplifies markedly due mainly to the Coriolis accelerationl_(t) sin φ_(k) {dot over (φ)}_(h) ², and the second modulation term({dot over (φ)}_(k)+{dot over (α)}), prevents a premature landing of theleg. This term compares the knee extension velocity to the approachvelocity {dot over (α)} (negative when moving forward). If the kneeextends faster than the leg moves towards its target angle, dampingtorque is proportionally activated; otherwise, no control torque isapplied.

The final knee control task of stopping swing and extending the leg intothe target is initiated when the leg angle passes a thresholdα_(thr)=α_(tgt)+Δα_(thr) and is realized with two functional components.The first component generates a stopping knee-flexion torque

$\begin{matrix}{\tau_{k}^{iii} = \left\{ \begin{matrix}{{{- {k^{stp}\left( {\alpha_{thr} - \alpha} \right)}}\left( {1 - \frac{\overset{.}{\alpha}}{{\overset{.}{\alpha}}_{\max}}} \right)},} & \begin{matrix}{{\alpha < \alpha_{thr}}\;} \\{\overset{.}{\alpha} < {\overset{.}{\alpha}}_{\max}}\end{matrix} \\{0,} & {otherwise}\end{matrix} \right.} & (8)\end{matrix}$

that is inspired by nonlinear contact models, where k^(stp) is aproportional gain, α_(thr)−α corresponds to ‘ground indentation’ and{dot over (α)}_(max) is the return velocity at which ‘ground resistance’vanishes. The stopping torque works well only if its coupling into thehip motion is canceled and we apply the compensation torque

τ_(h) ^(iii)=−2τ_(k) ^(iii)  (9)

at the hip. To motivate this particular compensation, consider equations1 and 2 at hip and knee angles of 180 deg (vertical leg position). Theequations then simplify to

(m _(t)+2m _(s))l _(t) ²{umlaut over (φ)}_(h)=τ_(h)+τ_(k) m _(s) l _(t)²{umlaut over (φ)}_(k)  (10)

m _(s) l _(t) ²{umlaut over (φ)}_(k)=τ_(k)+2m _(s) l _(t) ²{umlaut over(φ)}_(h)  (11)

where we used the assumption l_(s)=l_(t). Using equation 11 tosubstitute in {umlaut over (φ)}_(k) equation 10, we get

m _(t) l _(t) ²{umlaut over (φ)}_(h)=τ_(h)+2τ_(k)

for the hip equation, which shows that a compensation torqueτ_(h)=+2τ_(k) cancels the effect of knee torque on the hip motion.

The second functional component engages when the leg has slowed down tozero angular speed {dot over (α)}=0, upon which a deliberate extensioncomponent is added to the knee torque,

τ_(k) ^(iii′)=τ_(k) ^(iii) +k ^(ext)(l ₀ −l),  (12)

where k^(ext) is a proportional gain and l₀=l_(t)+l_(s). This activeknee extension ensures that the leg reaches down to the ground.

Results and Discussion

The control developed in the previous section is based on the simpledouble pendulum as a conceptual model (FIG. 1A). However, to test thecontrol performance, a swing leg model was used that considershuman-like segment mass distribution and the effect of hip translationalaccelerations generated by the body (FIG. 1B). With this more realisticmodel, the control parameters were tuned to achieve robust leg placementinto a realistic range of target angles assuming large variations ininitial conditions. The predicted patterns of the foot point motion andthe joint torques were then compared with those of human walking andrunning, and evaluated the quality of the leg placement generated by thelocal feedback control during sudden changes in swing leg targets aswell as during horizontal pushes on the foot point that simulateobstacle encounters.

A. Leg Placement into Arbitrary Targets

The initial leg configuration is set to φ_(h,0)=220 deg and φ_(k,0)=175deg (α₀=132.5 deg), the clearance leg length is fixed at l_(clr)=5 cm,and the control gains of the local feedback control are hand-tuned withthe goal of minimizing the error between the target leg angle and theactual landing angle for a large range of initial joint velocities andtarget angles. Simultaneously, peak joint torques are tuned to be withinthe peak torques observed in human walking and running. Note that thehip is still assumed to be hinged during tuning as it is unclear whatexternal translational accelerations should be applied in this process.The resulting set of control parameters is shown in Table 1.

TABLE 1 Control parameters values. Values in parentheses are gainsadapted for walking & running respectively. parameter value parametervalue k_(p) ^(α) 110 (50/150) Nmrad⁻¹ k^(i) 13 Nmsrad⁻¹ k_(d) ^(α) 8.5(5.5/8.5) Nmsrad⁻¹ k^(ii) 5.5 Nmsrad⁻¹ k^(stp) 250 (60/160) Nmrad⁻¹ {dotover (α)}_(max) 10 rads⁻¹ k^(ext) 200N α_(thr) α_(tgt) + 8 deg

FIG. 3 shows the resulting control performance for target anglesα_(tgt)=50 . . . 130 deg that include typical human landing leg anglesand for initial joint velocities {dot over (φ)}_(h,0)=−5 . . . 5 rads⁻¹and {dot over (φ)}_(k,0)=−10 . . . 0 rads⁻¹ that cover the experimentaldata on initial joint velocities in human locomotion ({dot over(φ)}_(h,0)=−4 . . . 2 rads⁻¹ and {dot over (φ)}_(k,0)=−7 . . . 1rads⁻¹). The identified feedback control can achieve low targetplacement errors with an average error of 1.4 deg and a maximum error of5.2 deg throughout the large ranges of target angles and initial jointvelocities. Similar results hold for different ground clearanceconstraints and initial leg configurations (l_(clr)=5, 8 . . . cm andα₀=132, 140 . . . deg).

B. Comparison to Human Walking and Running

For the comparison to human swing motions, multiple swing legtrajectories of a subject walking from 0.65 ms⁻¹ and 2 ms⁻¹ and runningfrom 2.5 ms⁻¹ to 5.5 ms⁻¹ were recorded, covering slow to fast walkingas well as slow to fast running. The left columns in FIGS. 4A-C and 5A-Cshow the ankle trajectories (A) and the corresponding hip and kneetorques (B and C, obtained from inverse dynamics) observed during humanswing in walking and running at the different speeds.

The model-predicted swing leg patterns are similar to the observed onesin walking. The right column in FIGS. 4A-C shows the model-predictedswing phase motion of the foot point (tip of shank segment) and thecorresponding joint torque patterns. (For all speeds, the model's targetangle is α_(tgt)=70 deg, which equals the observed landing angle α₁=70±3deg.) Also, hip translational accelerations are applied in the modelbased on the observed hip accelerations for each swing phase. As aresult, the hip control gains had to be adjusted to one set of lowervalues for all walking trials and of higher values for all runningtrials, Tab. 1) The foot point motion has a similar range and shape forall four walking speeds (A), and the hip and knee torques have similarmagnitudes and gross behavior (B and C). In the model, the hip torquepattern is generated by the target angle control (Eq. 4) throughoutswing, except for the sharp rise in hip extension torque which appearsin the second half of swing due to the knee compensation τ_(h)^(iii)=2τ_(k) ^(iii) (Eqs. 5 and 9). This sharp rise also occurs in theknee torque pattern and is generated by the knee stopping torque (Eq.8). One marked difference in the knee torque pattern appears at 2.00ms⁻¹ walking, where, before the knee damping occurs that prevents legflexion past the clearance length (Eq. 7), the model shows an initialknee flexion torque to actively prevent scuffing the foot (Eq. 6). Thisinitial flexion torque is not visible in human walking. The differenceis related to the much larger initial hip flexion torque that humans useat this speed, which passively flexes the knee and thus prevents footscuffing. It points to a speed-dependent increase in the hip controlgains not included in the model.

In contrast to walking, the predicted patterns for running have ashorter stride length and a clearly faster swing time than present inhuman running (FIGS. 5A-C). Despite these differences, the shapes of thetorque patterns match human data in general (B and C). The shape of thehip torque pattern is similar between walking and running in the model.Except for an initial modulation, this general shape is also preservedin the human hip torque pattern between walking and running. Bycontrast, the knee torque pattern shows an added, initial period ofsilence in running which is present in both the model and the humandata. This silent period occurs in the model as the initial knee anglein the swing phase of running (φ_(k,0)=149±2.5 deg) is more extendedthan in walking (φ_(k,0)=120±2 deg), and the knee passively flexesbefore the leg reaches the clearance length where the damping torqueengages (Eq. 7).

The short swing phase in running is caused mainly by an increasedproportional gain k_(p) ^(α) for the leg angle control at the hip (Eq. 4and Table 1). This modification in the model was required, becauseotherwise the passive leg flexion by the hip control is too weak and thelarge hip translational accelerations in running force the leg into anearly landing. The modification also entails a larger gain k^(stp) forthe stopping control (Eq. 8 and Table 1).

C. Reactions to Target Changes and Obstacle Encounters

In addition to comparing the predicted swing leg patterns to human swingmotions, the performance of the control in the presence of disturbanceswas tested. First, sudden changes in the target angle were considered.FIG. 6A shows the characteristic response of the model to changes in thetarget angle from α_(tgt)=50 deg to α_(tgt)=90 deg and vice versa (leftand right columns, respectively), which are initiated at 75 ms into theswing phase. In both cases, the control rapidly adapts and guides thefoot point into the new target position with negligible error. A similarperformance for the same changes initiated later in the swing wasobserved (not shown), up to 150 ms from 50 deg to 90 deg (at which theleg angle crosses_α=90 deg in the undisturbed swing) and up to 225 msfor the reverse change (which equals about 80% of the swing time of itscorresponding undisturbed case).

FIG. 6B shows the characteristic response of the model to an impulsedisturbance of 15 Ns in early and late swing (left and right columns).The impulse simulates obstacle encounters and is applied as a constantforce applied to the foot point in the negative x-direction. The modelshows an elevating response for the early disturbance and a prematurelanding for the late disturbance. Both responses are observed in humanlocomotion and often assumed to reflect two explicit control strategies.By contrast, the model shows these two behaviors as inherent outcomes ofits placement control.

The results of the exemplary embodiments suggest that the control canachieve swing leg placement into a large range of targets for a widerange of walking and running speeds with robustness to disturbances ininitial conditions and to sudden changes in the placement target duringswing. In the simulation model, the control achieves leg placement intotarget angles ranging from 50 deg to 130 deg with an average error of1.4 deg and a maximum error of 5.2 deg throughout a large range ofinitial joint velocities (FIG. 3B). This accuracy is maintained evenwhen the target angles are suddenly changed during swing (FIG. 6A). Thisperformance, generated by the developed control without the need totrack reference trajectories of either the hip or the knee joint, is instark contrast to current control approaches using trajectory tracking,which need to retune trajectories for different locomotion speeds and toprovide explicit compensation trajectories when encounteringdisturbances.

In addition, the control generates swing patterns that share the mainfeatures of human swing leg patterns. In undisturbed swings, the controlgenerates foot point and joint torque patterns that are similar to thosepatterns observed in human walking and running (FIGS. 4A-C and 5A-C).One major difference is the substantially shorter swing time in runningin the model, which coincides with clearly shorter stride lengths.During simulated obstacle encounters in early and late swing, the modelgenerates an elevating response and a premature landing, respectively(FIG. 6B). Both responses are well known behaviors in disturbed humanswing phases. In contrast to generating these responses with explicitlytriggered control, they are inherent to the identified leg placementcontrol.

Now turning to FIG. 7 that illustrates an overview of the system of thepresent invention. The present invention system includes sensory input10, swing leg controller 20, and control output 30, each incommunication with its adjacent sub-system module. Sensory input 10collects data from an Inertial measurement unit (IMU) 12 to determinethe current hip angle Φ_(H) and knee encoder 14 to determine currentknee angle Φ_(K), and swing phase sensor 16 having contact sensors (notshown) to determine contact of the foot with the ground identifying thebeginning and end of the swing phase. Sensory input 10 provides input toswing leg controller 20 for the calculation of key parameters discussedabove to determine the positive or negative hip torque 32 and kneetorque 34 to apply to the hip joint and/or the knee joint to satisfy acondition. The application of hip torque and knee torque is administeredby Control Output 30. The Inertial measurement unit 12 is an electronicdevice that measures and reports on an object's velocity, orientation,and gravitational forces, using a combination of accelerometers andgyroscopes, sometimes also magnetometers. The knee encoder 14 is anelectro-mechanical device that converts the angular position or motionof a shaft or axle to an analog or digital code.

Now turning to FIG. 8 that illustrates an implementation of the keymodules of the system. As discussed in FIG. 7, the IMU 12 determines thecurrent hip angle Φ_(H) and knee encoder 14 determines current kneeangle Φ_(K). Current leg angle α is determined from FIG. 2B based on thecurrent leg angle α. Current leg length l is calculated from the CosineLaw based on the current knee angle Φ_(K). The calculated current legangle α and current leg length l are input into Differentiator 40 todetermine the current leg angular speed {dot over (α)} and leglengthening speed. Memory 60, in communication with microprocessor 50,stores the controller parameters and the target leg angle α_(tgt).Microprocessor 50 uses the stored data in memory 50, current hip angleΦ_(H), current knee angle Φ_(K), current leg length l, and current legangle α along the state of the swing phase based on the contact sensorin communication with the swing phase control 16 to determine thepositive or negative torques to apply to knee actuator 80 and hipactuator 90 throughout the swing phase to place the foot on to thetarget position.

Now turning to FIG. 9 that illustrates a system schematic of the kneejoint control system of the present invention. There are four phases ofthe typical swing phase for the knee: Flex, Damp, Stop, and Extend. Theonset of the swing control is initiated when the foot is no longer incontact with the ground. Current leg angular speed {dot over (α)} (alsoknown as leg angle speed) is input into the Flex phase that utilizes Eq.6 for active knee flexion control applying the appropriate knee torque(no hip torque) until the current leg length 1 is less than or equal toclearance leg length l_(clr). The Damp phase, which follows the Flexphase, uses as input into Eq. 7 current leg angle α, current leg angularspeed {dot over (α)}, current leg length and current leg lengtheningspeed to apply the appropriate knee torque (no hip torque) until currentleg angle α is less than leg angle threshold α_(threshold). The Stopphase, which follows the Damp phase, uses as input into Eqs. 8 and 9current leg angle α and current leg angular speed {dot over (α)} toapply the appropriate knee torque (Eq. 8) and hip torque (Eq. 9) untilcurrent leg angular speed α is equal to or greater than zero. The Extendphase, which follows the Stop phase, uses as input into Eqs. 9 and 12current leg angle α and current leg angular speed {dot over (α)}, toapply the appropriate hip torque (Eq. 9) and knee torque (Eq. 12) untilthe foot contacts the ground activating the contact sensor indicatingthe end of the swing phase and the beginning of the stance phase.

FIG. 10 is a system schematic of the hip joint control system of thepresent invention. As mentioned above, the onset of the swing control isinitiated when the foot is no longer in contact with the ground. Thereare two phases of the typical swing phase for the hip: Move to Target(which is coincident with the Flex and Damp phases of the knee jointcontrol) and Move & Compensate (which is coincident with the Stop andExtend phases of the knee joint control). The Move to Target phase usesas input into Eq. 4 current leg angle α and current leg angular speed αto apply the appropriate hip torque until current leg angle α is lessthan leg angle threshold α_(threshold). The Move & Compensate phase,which follows the Move to Target phase, uses as input into Eq. 4 currentleg angle α and current leg angular speed {dot over (α)} to calculatespecific control input τ_(h) ^(α) and uses as input into Eq. 9compensating torque τ_(h) ^(iii) to calculate compensation torque. Thesetorques are added to determine the resultant torque (Eq. 5) to apply theappropriate hip torque τ_(h) until the foot contacts the groundactivating the constant sensor, indicating the end of the swing phaseand the beginning of the stance phase.

Now turning to FIG. 11 for a logic flow diagram of one embodiment of thepresent invention discussed above. The present invention monitors keyparameters including, but not limited to, those parameters listed inthis application. The knee swing phase is independent from the hip swingphase. The knee swing phase includes the flex phase, damp phase, stopphase, and extend phase. The hip swing phase includes the Move to TargetPhase and the Move & Compensate phase. The knee and hip swing phasesbegin when the foot leaves the ground as monitored by contact sensors.The knee and hip stance phases begin when the foot contacts the groundas monitored by contact sensors. The swings phases begin again when thefoot leaves the ground.

Neuromuscular Control Model

To compare the identified control with human swing leg behavior at thelevel of muscle activations, and to prepare a transfer to artificialpowered legs that can react like human limbs, a neuromuscular model ofthe human leg in swing was developed to embody the modular control withlocal muscle reflexes. In one embodiment, the model comprises threesegments connected by revolute joints. The segments have anthropomorphicmass and inertia properties and the joints represent hip, knee andankle. Nine Hill-type muscle models span these joints, each consistingof a contractile element CE, and parallel and series elasticities (FIG.12). A muscle produces the net force

F ^(m) =F _(max) ^(m) f _(l) f _(v) A ^(m)

that is dependent on its maximum isometric force F_(max) ^(m), theforce-length (f_(l)) and force-velocity relationships (f_(v)) of thecontractile element, and the muscle activation A^(m). The muscle forcetranslates into the joint torque contribution τ_(j) ^(m)=F^(m)r_(j) ^(m)at the joints j the muscle spans, where r_(j) ^(m) is the muscle momentarm. The activation is related to the neural stimulation S_(m)ε[0,1] ofa muscle by

{dot over (A)} ^(m)=(S ^(m) −A ^(m))τ_(ecc),

where the constant τ_(ecc)=10 ms describes the excitation-contractioncoupling of muscle tissue.

For the muscle reflex embodiment of the modular leg placement controldescribed in the preceding paragraphs the muscle stimulations aregenerated by local proprioceptive feedbacks from the same or othermuscles (general index n),

$\begin{matrix}{{{S^{m}(t)} = {S_{0}^{m} + {\sum\limits_{n}{G_{n}^{m}{P_{n}^{m}\left( {t - {\Delta \; t_{n}^{m}}} \right)}}}}},} & (13)\end{matrix}$

where S₀ ^(m) is the muscle prestimulation, G_(n) ^(m) is a feedbackgain, P_(n) ^(m) is the proprioceptive signal, Δt_(n) ^(m) representsthe neural transport delay, and the sum symbol describes α-motoneuronswhich can combine multiple feedbacks to generate the muscle netstimulation. The proprioceptive signals P_(n) ^(m). n are either lengthor velocity signals from the originating muscle n with

L _(n) ^(m) =l _(ce) ¹ −l _(off) ^(n) and V _(n) ^(m) =v _(ce) ^(n) −v_(off) ^(n),  (14)

respectively. The offset values l_(off) ^(n) and v_(off) ^(n) model setpoint adjustments that γ-motoneurons can generate at muscle spindles,the sensory organs which measure muscle length and velocity. Note thatthe muscle stimulation (Eq. 13) is saturated between zero and one,reflecting that neurons modulate signals with firing rates that cannotbecome negative.

A. Leg Angle Estimation with Biarticular Muscle Stretch

The control described in the previous section requires the leg angle asa main input. This quantity can be estimated in the human neuromuscularsystem by the length of two biarticular muscles, the hamstring (HAM) andthe rectus femoris (RF). Both muscles span the hip and knee. HAM is ahip extensor and knee flexor while RF flexes the hip and extends theknee. The lengths of the two muscles are given by

l ^(m) =l ₀ ^(m) ±r _(h) ^(m)(φ_(h)−φ_(h,r) ^(m))∓r _(k)^(m)(φ_(k)−φ_(k,r) ^(m))  (15)

where l₀ ^(m) is the muscle rest length that is reached at the legconfiguration defined by φ_(h,r) ^(m) and φ_(k,r) ^(m), and r_(h) ^(m)and r_(k) ^(m) are muscle moment arms at the hip and knee, respectively(top/bottom version for RF/HAM). In humans, r_(k) ^(m)≈r_(h) ^(m)/2 forRF and HAM, and the leg angle relates to the hip and knee angles byα≈φ_(h)−φ_(k)/2. Equation 15 thus simplifies to

l ^(m) =l ₀ ^(m) ±r _(h) ^(m)(α−α_(r) ^(m))

with α_(r) ^(m)=φ_(h,r) ^(m)−φ_(k,r) ^(m)/2. On the other hand, inmuscle l^(m)=l_(ce) ^(m)+l_(se) ^(m). Assuming that the serieselasticity does not stretch substantially beyond its slack length(l_(sl) ^(m)) in these muscles, l_(se) ^(m)=l_(sl) ^(m) (due to the lowforces required in swing), the leg angle resolves to α=±(l_(ce)^(m)+l_(sl) ^(m)−l₀ ^(m))/r_(h) ^(m)+α_(r) ^(m). Now, the controldescribed above requires leg angle inputs only as differences α−α_(i)with respect to target values α_(i), which resolves to

α−α_(i)=±1/r _(h) ^(m)(l _(ce) ^(m) −l _(off) ^(m))  (16)

when choosing the offset l_(off) ^(m)=±r_(h) ^(m)(α_(i)−α_(r)^(m))−l_(sl) ^(m)+l₀ ^(m). Equation (16) describes a muscle spindlelength feedback (Eqs. 13 and 14) of either the RF or the HAM. Likewise,the leg angular speed can be estimated by the spindle velocity feedbackof these biarticular muscles,

{dot over (α)}=±1/r _(h) ^(m)(v _(ce) ^(m) −v _(off) ^(m)) with v _(off)^(m)=0  (17)

B. Ankle Control

For the control of the added ankle, the same muscles and reflexes as inconventional prosthetic ankles are used. Three muscles actuate theankle, the monoarticular soleus (SOL) and tibialis anterior (TA) musclesas well as the biarticular gastrocnemius muscle (GAS) (FIG. 12A). Whilethe ankle extensors SOL and GAS do not actively contribute to anklecontrol in swing, TA gets stimulated by its own length feedbackS^(TA)=S₀ ^(TA)+S₀ ^(TA)+G_(TA) ^(TA)L_(TA) ^(TA) lifting the footsegment into the neutral position (right angle with the shank). Theparameter values for all gains and offsets are reported in Table 2.

C. Hip Control

The hip portion of the modular control (Eq. 5) was implemented bystimulating the hip extensor (gluteus group, GLU) and the hip flexor(HFL) (FIG. 3A), using the stretch feedback from RF for HFL and from HAMfor GLU,

S ^(HFL)(t)=S ₀ ^(HFL) +G _(RF) ^(HFL) L _(RF) ^(HFL)(t−Δt _(RF)^(HFL)),  (18)

S ^(GLU)(t)=S ₀ ^(GLU) +G _(HAM) ^(GLU) L _(HAM) ^(GLU)(t−Δt _(HAM)^(GLU)),  (19)

We thus separate the flexion and extension part of the commanded torquein (Eq. 5) observing that muscle can only pull in general and that HAMand RF in particular can go slack when the leg points backward andforward, respectively. Due to (Eq. 16), the two stretch feedbacksjointly represent the first term in (Eq. 5). We do not implement thesecond term with explicit neuromuscular control since the muscles'force-velocity relationship A, automatically realizes a dampingbehavior. We detail how we realize the last, knee-hip-interaction termof (Eq. 5) in the next section on knee control.

TABLE 2 Control parameter values. Other parameters are known by thoseskilled in the art. Gains Offsets G_(TA) ^(TA) 25 G_(BFsH) ^(BFsH) 1.25l_(off) ^(RF)  0.059 (m) G_(RF) ^(HFL) 0.5 G_(HAM) ^(HAM) 2 l_(off)^(HAM) 0.0716 (m) G_(HAM) ^(GLU) 0.5 G^(HAM) _(BFsH) 3 l_(off) ^(VAS)0.0324 (m) G_(RF) ^(BFsH) 0.1 G_(HAM) ^(GAS) 2 l_(off) ^(TA) 0.0432 (m)G_(VAS) ^(RF) 0.14 G_(VAS) ^(VAS) 0.05 S_(thr) 0.65

D. Knee Control

The neuromuscular embodiment of the knee control follows along with thethree natural control tasks. We realize the first task by stimulatingthe short head of biceps femoris (BFsH), a monoarticular knee flexor,with a velocity feedback (Eq. 17) from RF,

S ^(BFsH,i)(t)=G _(RF) ^(BFsH) V _(RF) ^(BFsH)(t−Δt _(RF)^(BFsH)),  (20)

using v_(off) ^(RF=0) (FIG. 12B). The zero offset automaticallygenerates the velocity condition in (Eq. 6) as the resulting musclestimulation is bound to positive values.

For the second control task, we implement a length feedback L^(VAS) ofthe vasti (VAS), a group of monoarticular knee extensors. This feedbackhas no target muscle; it monitors leg length and engages the reflexesfor the second task once the leg achieves sufficient ground clearancel<l_(clr). (In humans, l∝φ_(k) and φ_(k)−φ_(k,i)=∓1/r_(k) ^(m)(l_(ce)^(m)−l_(off) ^(m)) and {dot over (φ)}_(k)=∓1/r_(k) ^(m)(v_(ce)^(m)−v_(off) ^(m)) for monoarticular knee extensors/flexors). During thesecond task, we realize the extension part (first line of Eq. 3) bystimulating RF with a velocity feedback from VAS

S ^(RF,ii)(t)=G _(VAS) ^(RF) V _(VAS) ^(RF)(t−Δt _(VAS) ^(RF)).  (21)

For the flexion part (second and third line), BFsH is simulated with itsown velocity feedback,

S ^(BFsH,ii)(t)=G _(BFsH) ^(BFsH) V _(BFsH) ^(BFsH)(t−Δt _(BFsH)^(BFsH))M,  (22)

where M are modulating reflexes with M=L_(RF) ^(BFsH)(t−Δt_(RF)^(BFsH))·[v_(BFsH) ^(BFsH)(t−Δt_(BFsH) ^(BFsH))+v_(RF) ^(BFsH)(t−Δt_(RF)^(BFsH))].

The first modulation reflex from the biarticular RF implements the term(α−α_(tgt)) of (Eq. 7). The other modulation term in this equation,({dot over (φ)}_(k)+{dot over (α)}), is implemented using the sum of twovelocity reflexes from BFsH for {dot over (φ)}_(k) and from RF for {dotover (α)}. These velocity reflexes also implicitly ensure the condition{dot over (φ)}_(k)>{dot over (α)} for generating flexion torque.

The final control task of braking and extending the leg is implementedprimarily by stimulating HAM and VAS (FIG. 3B). We use the biarticularstretch reflex

S ^(HAM,ii)(t)=G _(HAM) ^(HAM) V _(HAM) ^(HAM)(t−Δt _(HAM) ^(HAM))  (23)

to stimulate HAM, which mimics the term (α_(thr) a) of (Eq. 8) whenusing the offset value

l _(off) ^(HAM) =−r _(h) ^(HAM)(α_(thr)−α_(r) ^(HAM))−l _(sl) ^(HAM) +l₀ ^(HAM).

In addition, HAM proportionally recruits the synonymous knee flexorsBFsH and GAS once its stimulation exceeds a thresholdS^(HAM,iii)>S_(thr),

S ^(BFsH,iii)(t)=G _(HAM) ^(BFsH) [S ^(HAM,iii)(t)−S _(thr)],  (24)

S ^(GAS,iii)(t)=G _(HAM) ^(GAS) [S ^(HAM,iii)(t)−S _(thr)],  (25)

to prevent hyper extension of the knee caused by HAM torque saturationat high swing leg angular speeds. The second, velocity term of (Eq. 8)is neglected in the control as the HAM's force-velocity relationshipproduces a similar damping behavior. However, we use a passive velocityfeedback V^(HAM) to monitor when the leg angular speed has slowed downto zero (α=0), which triggers VAS stimulation by its own stretch reflex,

S ^(VAS,iii)(t)=G _(VAS) ^(VAS) L _(VAS) ^(VAS)(t−Δt _(VAS)^(VAS)),  (26)

to extend the knee.

Although the muscle reflexes are introduced along with the three controltasks, they are active throughout swing without the separation intotask-related phases. For instance, the total stimulation of BFsH isgenerated by S^(BFsH,tot)=S^(BFsH,i)+S^(BFsH,ii)+S^(BFsH,iii). The onlyexception is the VAS extension reflex, which is connected only after{dot over (α)}=0 in the last task.

Results and Discussion

A. Leg Placement into Arbitrary Targets

The control parameters of the neuromuscular model were tuned by handwith two goals in mind. First, with the application to autonomousprostheses in mind, a single set of parameters that minimizes the errorbetween the landing leg angle and its target α_(tgt) for a large rangeof initial joint velocities and target angles exceeding those of humanwalking and running were sought after. Second, it was required that thecorresponding joint torques to stay within experimentally observedranges.

The identified set of control parameters is shown in Table 2. Except forα_(thr), which differs between walking and running (12/24 degrespectively), parameters remain constant. The larger threshold anglefor activating HAM earlier in running than in walking is needed toprevent knee hyper-extension. Such an earlier activation is alsoobserved in humans.

The achieved performance of target placement with the neuromuscularsystem is shown in FIG. 13. For target angles α_(tgt)=50 . . . 75 degand for initial joint velocities {dot over (φ)}_(h,0)=−5 . . . 5 rads⁻¹and {dot over (φ)}_(k,0)=−10 . . . 0 rads⁻¹, the average and maximumplacement errors are 2.8 deg and 9.2 deg. These errors compare with theperformance of the ideal control and cover typical human landing legangles and initial joint speeds observed in walking and running. Forsteeper target angles, however, the placement shows clearly larger errordue to the toe dragging the ground.

B. Comparison to Human Walking and Running

In another example, the resulting swing leg motions were compared toactual human leg motions. The swing leg trajectories of a subjectwalking at slow to fast speeds (0.65 ms⁻¹ to 2 ms⁻¹) and running at slowto moderately fast speeds (2.5 ms⁻¹ to 5.5 ms⁻¹) were recorded. Thesubject's ankle trajectories and corresponding hip and knee torquesduring swing are shown in the left column of FIGS. 14A-F. The rightcolumn shows the patterns predicted by the neuromuscular model. (Notethat for the comparison the observed hip translational accelerations andleg initial conditions were applied to the model.) In addition, FIGS.16A-C compare the time history of muscle activations generally observedin walking and running with those predicted by the model for matchedspeeds.

In walking, the swing leg patterns predicted by the model are similar tothe ones observed in humans. The ankle trajectories have a similar rangeand shape in particular for slower walking speeds (FIG. 14A), and thehip and knee torques have similar magnitudes and gross behavior exceptfor the larger initial torques in human walking at 2 ms⁻¹ (FIGS. 14B and14C). The activation patterns for the hip muscles HFL and GLU showsimilar timings and magnitudes between the model and humans (FIG. 15A).Although the knee muscle activation patterns show a similar trend (FIG.15B), some deviations occur with respect to the onset time for BFsH,which is delayed. For the ankle muscles, TA misses the late swingactivation seen in humans in preparation for stance (FIG. 15C), a knownshortcoming of an example ankle control.

In contrast to walking, the patterns for running show more deviationsbetween the model and humans. The model has a shorter stride length anda clearly faster swing time than present in human running (FIG. 14D).Despite these differences, the shapes of the torque patterns match humandata in general (FIGS. 14E and 14F). In the activation patterns, humanshave an increased tonus for all muscles that is absent in the model(FIGS. 15A-C). In addition to this muscle tonus, the activities of BFsHand GAS show different characteristic features. In humans, BFsH has aprominent activation peak that coincides with RF peak activation (FIG.15B). By contrast, in the model, the early BFsH peak occurs at the verybeginning of swing and RF activity onset is delayed. Further, the modelshows an activation burst of GAS at the end of swing due to thesynonymous activation (Eq. 25) that humans do not seem to have to suchan extent (FIG. 15C).

FIGS. 16-24 describe example implementation of the swing leg controller(FIG. 7) with an algorithm that emulates human neuromuscular control,taking sensory input about hip and knee angles as well as swing phasedetection and converting this input into hip and knee joint torquecommands.

FIGS. 16 and 17 describe how the algorithm translates sensor inputs froman IMU (hip angle) and a knee encoder (knee angle) into estimates of legangle and leg angular speed (FIG. 16) as well as leg length and leglengthening speed (FIG. 17).

In FIG. 16, joint angle information from the hip and knee sensors isconverted into the length of a virtual muscle that spans both joints(GEOMETRY). This virtual muscle represents either the hamstring (HAM) orthe rectus femoris (RF). Together with a virtual muscle stimulation thatis provided by the algorithm described in FIG. 18 and gets convertedinto muscle activation (ACTIVATION DYNAMICS), the resulting musclelength and velocity is computed (MUSCLE TENDON MODEL). From this virtualmuscle length and velocity information, the current leg angle (ANGLEESTIMATE) and current leg angular speed (SPEED ESTIMATE) of the swingleg are estimated. The offsets for the muscle length (l_off̂m) andvelocity (v_off̂m) are control parameters of the algorithm and providedby the designer.

In FIG. 17, joint angle information from the knee sensor is convertedinto the length of a virtual muscle that spans the knee joint(GEOMETRY). This virtual muscle represents either the vastii group (VAS)or the biceps femoris short head (BFSH). Together with a virtual musclestimulation that is provided by the algorithm described in FIG. 18 andgets converted into muscle activation (ACTIVATION DYNAMICS), theresulting muscle length and velocity is computed (MUSCLE TENDON MODEL).From this virtual muscle length and velocity information, the currentleg length (LENGTH ESTIMATE) and current leg lengthening speed (SPEEDESTIMATE) of the swing leg are estimated. The offsets for the musclelength (l_off̂m) and velocity (v_off̂m) are control parameters of thealgorithm and provided by the designer.

FIGS. 18 and 19 describe how the algorithm converts the estimates of legangle, leg angular speed, leg length, and leg lengthening speed intomuscle stimulations S_m of six virtual leg muscles m (BFSH, RF, HAM,GAS, VAS, HFL, GLU). These muscle stimulations contribute in a virtualfeedback loop to the generation of the estimates of leg angle, legangular speed, leg length, and leg lengthening speed (FIGS. 16 and 17).The muscle stimulation signals are also used to compute hip and kneetorques contributed by the individual muscles (FIGS. 20, 21 and 22).

FIG. 18 shows a schematic of this conversion for the knee joint control.The conversion is separated into the four control phases described inFIG. 9. The initial FLEX phase engages when the swing phase sensordetects the onset of swing. In the FLEX phase, the estimate of legangular speed d_alpha using the virtual muscle RF is used to generatethe muscle stimulation of the virtual muscle BFSH according to equation13. The estimate of leg length l using the virtual muscle VAS is usedduring this phase to continuously check if the leg length has contractedbelow the clearance length l_clr (FIG. 2C). Once 1<l_clr, the algorithmenters the DAMP phase, and virtual muscle stimulations of RF and BFSHare computed according to equations 14 and 15 using the estimate of leglengthening speed from VAS and BFSH (FIG. 17), and the estimate of legangle and leg angular speed from RF (FIG. 16). Throughout the DAMPphase, the estimate of the leg angle using the virtual muscle HAM (FIG.16) is used to continuously check if the leg angle alpha is below thethreshold alpha_threshold (FIG. 2C). Once alpha<alpha_threshold, thealgorithm enters the STOP phase. In the STOP phase, the estimate of theleg angle alpha using HAM (FIG. 16) is used to compute the stimulationof HAM according to equation 16. In addition the resulting HAMstimulation is used to compute the stimulation of BFSH according toequation 17. Throughout the STOP phase, the estimate of the leg anglevelocity using the virtual muscle HAM (FIG. 16) is used to continuouslycheck if the leg angle velocity d_alpha has reversed to positive values(FIG. 2C). Once d_alpha>=0, the algorithm enters the EXTEND phase, andthe stimulations of the virtual muscles BFSH, HAM and VAS are computedaccording to equations 16, 17 and 19 using the estimate of leg anglefrom HAM (FIG. 16) and the estimate of leg length from VAS (FIG. 17).The EXTEND phase ends when the swing phase sensor detects the onset ofstance.

FIG. 19 shows a schematic of the conversion from estimated leg angle andangular speed to virtual muscle stimulations for the hip flexor andextensor muscles (HFL and GLU). The initial MOVE TO TARGET phase startswhen the swing phase sensor detects the onset of swing. During thisphase, the algorithm computes according to equation 11 the stimulationof the virtual hip flexor muscle HFL using the estimate of the leg anglealpha from RF (FIG. 16). Throughout this phase, the leg angle estimatefrom HAM (FIG. 16) is used to continuously check if the leg angle alphais below the threshold alpha_threshold (FIG. 2C). Oncealpha<alpha_threshold, the algorithm enters the MOVE 86 COMPENSATEphase. In this phase, the estimate of the leg angle from HAM (FIG. 16)is used to compute the stimulation of the virtual hip extensor muscleGLU according to equation 12. The MOVE & COMPENSATE phase ends when theswing phase sensor detects the onset of stance.

FIGS. 20, 21 and 22 schematically describe how the algorithm convertsstimulations of the virtual muscles into desired torque contributionsabout the hip and knee joint by these muscles.

FIG. 20 describes this conversion for the virtual biarticular muscles(HAM and RF). Joint angle information from the hip and knee sensors isconverted into the length of a virtual muscle that spans both joints(GEOMETRY). Together with a virtual muscle stimulation that is providedby the algorithm described in FIG. 18 and gets converted into muscleactivation (ACTIVATION DYNAMICS), the resulting muscle force is computed(MUSCLE TENDON MODEL). This muscle force F_m is converted into torquecontribution to the hip (FORCE TORQUE CONVERSION) accordingtau_m̂h=F_m*r_ĥm. The moment arm r_ĥm is a control parameter of thealgorithm and provided by the designer. The muscle force F_m is alsoconverted into a torque contribution to the knee (FORCE TORQUECONVERSION) according tau_m̂k=F_m*r_k̂m. The moment arm r_k̂m is a controlparameter of the algorithm and provided by the designer.

FIG. 21 describes the conversion from muscle stimulation to joint torquecontribution for the virtual muscles that span only the hip (GLU andHFL). Joint angle information from the hip sensor is converted into thelength of a virtual muscle that spans the hip (GEOMETRY). Together witha virtual muscle stimulation that is provided by the algorithm describedin FIG. 19 and gets converted into muscle activation (ACTIVATIONDYNAMICS), the resulting muscle force is computed (MUSCLE TENDON MODEL).This muscle force F_m is converted into torque contribution to the hip(FORCE TORQUE CONVERSION) according tau_m̂h=F_m*r_ĥm. The moment arm r_ĥmis a control parameter of the algorithm and provided by the designer.

FIG. 22 describes the conversion from muscle stimulation to joint torquecontribution for the virtual muscles that span only the knee (BFSH andVAS). Joint angle information from the knee sensor is converted into thelength of a virtual muscle that spans the hip (GEOMETRY). Together witha virtual muscle stimulation that is provided by the algorithm describedin FIG. 18 and gets converted into muscle activation (ACTIVATIONDYNAMICS), the resulting muscle force is computed (MUSCLE TENDON MODEL).This muscle force F_m is converted into torque contribution to the knee(FORCE TORQUE CONVERSION) according tau_m̂k=F_m*r_k̂m. The moment arm r_k̂mis a control parameter of the algorithm and provided by the designer.

FIGS. 23 and 24 describe schematically how the algorithm computesdesired hip and knee torques from the muscle torque contributions.

FIG. 23 shows this computation for the hip joint. The summed torquecontributions of the hip flexor muscles (RF and HFL) are subtracted fromthe summed torque contributions of the hip extensor muscles (GLU andHAM), generating the desired hip torque tau_h of the swing legcontroller.

FIG. 24 shows the computation of the desired knee joint torque. Thesummed torque contributions of the knee flexor muscles (BFSH and HFL)are subtracted from the summed torque contributions of the knee extensormuscles (GLU and HAM), generating the desired knee torque tau_k of theswing leg controller.

While the disclosure has been described in detail and with reference tospecific embodiments thereof, it will be apparent to one skilled in theart that various changes and modifications can be made therein withoutdeparting from the spirit and scope of the embodiments. Thus, it isintended that the present disclosure cover the modifications andvariations of this disclosure provided they come within the scope of theappended claims and their equivalents.

1. A model-based limb controller for a limb comprising at least onerobotic limb joint, the controller comprising: a non-neuromuscular modelincluding a swing leg model and dynamic equations, wherein thenon-neuromuscular model is configured to receive feedback data relatingto a measured state of the limb and, using the feedback data and theswing leg model and the dynamic equations to determine at least onetorque command to be applied to the at least one robotic limb joint; anda torque control system in communication with the non-neuromuscularmodel, wherein the torque control system receives the at least onetorque command from the non-neuromuscular model for controlling the atleast one robotic limb, whereby motion of the at least one robotic limbjoint is determined without enforcing reference trajectories of the atleast one robotic limb joint.
 2. The controller of claim 1, furthercomprising at least one sensor mounted in proximity of the at least onerobotic limb joint to provide the feedback data to the at least onerobotic limb joint.
 3. The controller of claim 1, wherein the at leastone robotic limb joint is only an artificial knee joint.
 4. Thecontroller of claim 1, wherein the at least one robotic limb joint is anartificial knee joint and an artificial hip joint.
 5. The controller ofclaim 1, wherein at least one sensor is selected from the groupconsisting of an angular joint displacement, a velocity sensor, a torquesensor, and an inertial measurement unit.
 6. A method for controlling alimb comprising at least one robotic limb joint, the method comprisingthe steps of: receiving feedback data relating to a state of the limb;determining at least one joint torque to be applied to the at least onerobotic limb joint based on the state of the limb using anon-neuromuscular model comprising a swing leg model and dynamicequations; and applying the at least one joint torque determined by thenon-neuromuscular model processor at the at least one robotic limbjoint, whereby motion of the at least one robotic limb joint isdetermined without enforcing reference trajectories of the at least onerobotic limb joint.
 7. The method according to claim 6, wherein the atleast one robotic limb joint is only a robotic knee joint.
 8. The methodaccording to claim 6, wherein the at least one robotic limb joint is arobotic knee joint and a robotic hip joint.
 9. The method according toclaim 6, wherein the state of the limb is selected from the groupconsisting of a current hip rotation angle (φ_(h)) and a current kneerotation angle (φ_(k)).